Here is the full list of all 15 Risk of Rain achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Drown 20 Whorls.
Bank 20,000 gold.
Find the bloated survivor.
Find the robot janitor.
Collect 15 Monster Logs.
Deal 5000 damage in one shot.
Die 50 times.
Unlock a golden chest with the Explorer's Key.
Collect 4 Keycards.
Survive 40 minutes.
Pass a shrine 4 times in a row.
Kill a boss with 'Lights Out'.
Fail a shrine 3 times in a row.
Kill the Magma Worm, Wandering Vagrant, and Giant Stone Golem.
Defeat 20 lemurians in one playthrough.